Question

Plug variables expressed in SI units in the kinematic equation given in article: a = -v0^2/(2sg). What value of g you get as expressed in g's where g = 9.8 m/s^2 1 point the same as in English units smaller larger this calculation cannot be performed in SI units If the initial velocity of player is doubled then the absolute acceleration would * 1 point decrease 2x stays the same increase 2x increase 4x If stopping distance is decreased 2x then the acceleration would * 1 point decrease 2x stay the same increase 2x increase 4x Other: Hockey player having initial velocity 20 m/s and helmet having padding 5 cm hits head on his twin brother. The acceleration of his brain is most closely equal to * 1 point 0.4g 4g 40g 400g

Answer 1

Answer:

1) acceleration is increased by a factor of four 4X

2) the acceleration increases a factor of 2X

3) the correct answer of 400g

Explanation:

This is a kinematics exercise, where you use the velocity equation to obtain the acceleration, with the final velocity equal to zero.

           v² = v₀² + 2 a x

           0 = v₀² + 2 a x

           a = - v₀² / 2 x

           

In the case of wanting to give the acceleration as a function of g, we can find the relationship between the two quantities

         a / g = - v₀² / (2 x g)

Let's answer the different questions about this equation

1. The initial velocity is doubled, how much the acceleration is worth

           

       a/g = - (2v₀) 2 / 2xg

       a = 4 (-v₀² / 2xg) g

acceleration is increased by a factor of four 4X

2. if the stopping distance is reduced by 2, that is, x = x₀ / 2

we substitute

        a/g = (- v₀² / 2g) 2/x

         

        a =2  (-v₀² / 2x₀g)  g

       

therefore the acceleration increases a factor of 2X

3. the initial velocity of the hockey player is v₀ = 20 m / s and the stopping distance is

x = 5cm = 0.05m

we calculate the acceleration

        a / g = - 20² / (2 0.05)

        a / g = - 4000 / g

        a / g = - 4000 / 9.8 = 408

        a = 408 g

the correct answer of 400g, the value matches exactly if g = 10 m / s2 is taken